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Estimation of partially linear regression models under the partial consistency property

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  • Cui, Xia
  • Lu, Ying
  • Peng, Heng

Abstract

Utilizing recent theoretical results in high dimensional statistical modeling, a flexible yet computationally simple approach is proposed to estimate the partially linear models. Motivated by the partial consistency phenomena, the nonparametric component in the partially linear model is modeled via incidental parameters and estimated by a simple local average over small partitions of the support of the nonparametric variables. The proposed least-squares based method seeks to strike a balance between computation burden and efficiency of the estimators while minimizing model bias. It is shown that given inconsistent estimators of the nonparametric component, square root-n consistent estimators of the parameters of the parametric component can be obtained with little loss in efficiency. Moreover, conditional on the parametric estimates, an optimal estimator of the nonparametric component can be obtained using classic nonparametric methods. The statistical inference problems regarding the parametric parameters and a two-population nonparametric testing problem regarding the nonparametric component are considered. The results show that the behavior of the test statistics is satisfactory. To assess the performance of the new method in comparison with other methods, three simulation studies are conducted and a real data set about risk factors of birth weights is analyzed.

Suggested Citation

  • Cui, Xia & Lu, Ying & Peng, Heng, 2017. "Estimation of partially linear regression models under the partial consistency property," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 103-121.
    • Handle: RePEc:eee:csdana:v:115:y:2017:i:c:p:103-121
    DOI: 10.1016/j.csda.2017.05.004
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    References listed on IDEAS

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    1. Schick, Anton, 1996. "Root-n consistent estimation in partly linear regression models," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 353-358, August.
    2. Jianqing Fan & Wenyang Zhang, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying‐coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731, December.
    3. Jeffery Racine & Jeffrey Hart & Qi Li, 2006. "Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 523-544.
    4. Fan, Jianqing & Peng, Heng & Huang, Tao, 2005. "Semilinear High-Dimensional Model for Normalization of Microarray Data: A Theoretical Analysis and Partial Consistency," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 781-796, September.
    5. Li, Qi, 1996. "On the root-N-consistent semiparametric estimation of partially linear models," Economics Letters, Elsevier, vol. 51(3), pages 277-285, June.
    6. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
    7. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    8. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    9. Ming-yen Cheng & Hau-tieng Wu, 2013. "Local Linear Regression on Manifolds and Its Geometric Interpretation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1421-1434, December.
    10. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    11. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
    12. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
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    Cited by:

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    3. Liang, Weijuan & Zhang, Qingzhao & Ma, Shuangge, 2023. "Locally sparse quantile estimation for a partially functional interaction model," Computational Statistics & Data Analysis, Elsevier, vol. 186(C).

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